Selecting the right technique to predict disease from symptoms
I think you're coming at your problem slightly wrong... what you're essentially talking about is a belief network.
You may want to look into existing Bayesian Learning techniques to get your head around this, but belief networks commonly use the exact scenario you're talking about; using a set of known (or uncertain facts) statements to produce some inferred probability of a particular output.
Even more, they often express this through disease-symptom based examples in tutorials! Try here.
My point is that it would be better to use a belief network as the theoretical groundwork is all already there for you, instead of an ANN.